I own a 2 storey maisonette over a seperate flat below. Each of us has our own separate entrance . Leading from my front door is the stairs to my accommodation. I have fire doors throughout, fitted by the previous owner but wondered  if it is possible to fit a fire door either at the bottom or preferably the top of the stairs,the stairs come up the middle with rooms either side ,as Im always concerned about visitors falling if unsure or the layout. 

If you own it and you are going above legal requirement's with extra fire doors then it shouldn't be a problem. Technically it should go through Local Authority Building Control as it would be termed building work although I'm sure many owner/occupiers don't (which can catch them out when it comes to sell in future)